Blair & Rosen, Inc. (B&R) is a brokerage firm thatspecializes in investment portfolios designed to meet the specificrisk tolerances of its clients. A client who contacted B&R thispast week has a maximum of $50,000 to invest. B&R's investmentadvisor decides to recommend a portfolio consisting of twoinvestment funds: an Internet fund and a Blue Chip fund. TheInternet fund has a projected annual return of 12%, while the BlueChip fund has a projected annual return of 9%. The investmentadvisor requires that at most $35,000 of the client's funds shouldbe invested in the Internet fund. B&R services include a riskrating for each investment alternative. The Internet fund, which isthe more risky of the two investment alternatives, has a riskrating of 6 per thousand dollars invested. The Blue Chip fund has arisk rating of 4 per thousand dollars invested. For example, if$10,000 is invested in each of the two investment funds, B&R'srisk rating for the portfolio would be 6(10) + 4(10) = 100.Finally, B&R developed a questionnaire to measure each client'srisk tolerance. Based on the responses, each client is classifiedas a conservative, moderate, or aggressive investor. Suppose thatthe questionnaire results classified the current client as amoderate investor. B&R recommends that a client who is amoderate investor limit his or her portfolio to a maximum riskrating of 240.
| (a) | Formulate a linear programming model to find the bestinvestment strategy for this client. |
| | Let I | = Internet fund investment in thousands | | B | = Blue Chip fund investment in thousands |
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| If required, round your answers to two decimal places. If theconstant is \"1\" it must be entered in the box. If your answer iszero enter “0â€. |
| | - Select your answer -MaxMinItem 1 | I | + | B | | | | | s.t. | | | | | | | | I | + | B | - Select your answer -≤≥=Item 6 | | Available investment funds | | I | + | B | - Select your answer -≤≥=Item 10 | | Maximum investment in the internet fund | | I | + | B | - Select your answer -≤≥=Item 14 | | Maximum risk for a moderate investor | | | | I, B | - Select your answer -≤≥=Item 16 | | |
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| (b) | Build a spreadsheet model and solve the problem using Solver.What is the recommended investment portfolio for this client? |
| | Internet Fund | = | $ | | Blue Chip Fund | = | $ |
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| What is the annual return for the portfolio? |
| $ |
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| (c) | Suppose that a second client with $50,000 to invest has beenclassified as an aggressive investor. B&R recommends that themaximum portfolio risk rating for an aggressive investor is 320.What is the recommended investment portfolio for this aggressiveinvestor? |
| | Internet Fund | = | $ | | Blue Chip Fund | = | $ | | Annual Return | = | $ |
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| (d) | Suppose that a third client with $50,000 to invest has beenclassified as a conservative investor. B&R recommends that themaximum portfolio risk rating for a conservative investor is 160.Develop the recommended investment portfolio for the conservativeinvestor. If your answer is zero enter “0â€. |
| | Internet Fund | = | $ | | Blue Chip Fund | = | $ | | Annual Return | = | $ |
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